In an open-end spinning machine, the feed roller is rotated at a slow speed during the spinning operation. Thus, at the time of stopping the spinning operation, the feed roller may be stopped speedily by switching off the drive source. However, the combing roller is rotated during the spinning at a speed higher than 8,000 r.p.m. and thus it keeps on rotating for some time after the driving source is switched off. After the rotation of the feed roller is terminated, a certain amount of sliver is left on the surface of the feed roller. Since the combing roller is rotated by inertia, the sliver is fed little by little into the spinning rotor, as it is subjected to the combing action. The fiber thus supplied into the rotor is spun by the inertia rotation of the rotor into a long tennuous yarn which is connected integrally to the end of the spun yarn, as shown in FIG. 1. When the terminal yarn portion of such shape is fed into the rotor as an end yarn at the next spinning operation, it may not be entangled with the sliver at all or at least the yarn terminal portion will not be united evenly with the sliver.